H. A. Rowland—Concave Gratings for Optical Purposes. 95 
of the circular are of the grating: the hele is whether any 
The condition for theoretical perfection is that C shall remain 
constant for all portions of the mirror. I shall therefore inves- 
angles and y, and », the angles referred to the center of the 
muror. The condition is that . 
ote cay i 
sen sin “4+sin v 
= bone be a constant for all parts of the surface of the grating. 
et us then develop sin p and sin» in terms of #4, ¥, and the 
a 0 between the radii drawn to the center of the grating 
to the* point under consideration. Let 6 be the angle 
etween Rand R,. Then we can write immediately 
psin u=psin “, cos 6’ +R, sin 6’—p cos HW, sin 6” 
sin “=sin , cos 6 | 1+ R, A tan 6’ 
p sin ff, 
where Aix poe Fo 
= : 
